Closed-form unit-normalisation and orthogonality check of the SU(2) Clebsch–Gordan decomposition (½)⊗(½) = 1 ⊕ 0 on the canonical basis. Singlet |0,0⟩ = (|↑↓⟩−|↓↑⟩)/√2: norm² = (1/√2)² + (−1/√2)² = 1/2 + 1/2 = 1 (canonical sympy string…
Closed-form unit-normalisation and orthogonality check of the SU(2) Clebsch–Gordan decomposition (½)⊗(½) = 1 ⊕ 0 on the canonical basis. Singlet |0,0⟩ = (|↑↓⟩−|↓↑⟩)/√2: norm² = (1/√2)² + (−1/√2)² = 1/2 + 1/2 = 1 (canonical sympy string…